Hmmm, that is true but going on the same reasoning we can now follow the complete orbit of Halley's comet. Apparently there is one arcsecond difference between the predicted position and the observed one at present. Would be interesting if the two could somehow be related.

I guess what I'm trying to say is, if the pioneers were unpowered and we can't communicate with them, why not use something else out there that we can track?? 8-[

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MrObvious

Another of my famous speculations: If the sun ejects material in the way of solar wind and gravity wants to pull it back, then doesn't it create a cloud at the point of equilibrium? Going on the same notion I can't imagine all the hydrogen that initialy formed the sun went into it and the planets. Upon the suns ignition wouldn't the rest of it be in a state of equilibrium considering the pressure of light (from the sun) and the solar wind creating a halo of hydrogen? 8-[

If so then someone with the required knowledge and skill would be able to calculate the distance this would occur at.

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MrObvious

I'm only making an 'educated' guess here, but Pioneers may slow down enough to eventually go into some distant orbit around the Sun, possibly join all the other floatsam and jetsam from our solar system stuck in the Oort Cloud way past Pluto. Or, it might end up in a highly elliptical orbit same as some comets. Either way, it is very unlikely our distant space probes, Voyager included, will ever make it to the stars without additional thrust, if it turns out that G is progressively greater out there than it is here. :-({|=| Might want to attach a two-way probe to Hailey's next time around?

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Caveat Lector. Experimentum summus judex...

Couple of things:
Pioneer 10 & 11 are not moving back into an orbit toward the Sun and the vicinity of Earth or stuck in a very large distant orbit. They are leaving the solar system. We will never see them again, (unless we invent warp drive or something.) The term "anomalous acceleration towards the sun" refers to a detected pull on the space probes of 10 billion times smaller than the "acceleration" we feel from Earth's gravitational pull. This anomaly was detected from careful analyses of the nature of radio data.

It is also believed that in 1992 Pioneer 10 may have been deflected by close approached to an unknown, unseen Kuiper belt object at 56 AU from us. The object may have since been discovered by a team at Queen Mary and Westfield College in London, but awaits confirmation by other astronomers.

Barring unforeseen circumstances, Pioneer 11 will pass near one of the stars in the constellation Aquila in 4 million years. I'm not sure it will experience any detectible "anomalous acceleration towards the sun" by that time. It will likely be experiencing an new acceleration toward a new star by then. :wink: Pioneer 11 is silent to us.

Pioneer 10 is about 85 AU from the Sun and still inside the Kuiper Belt. Pioneer 10 is leaving the solar system over many more years. I am not sure which star system it is now headed toward.

The anomalous gravitational effect is still not fully understood but from what I've read, it will likely have an explanation that does not contradict conventional physics.

More interesting information can be found here: http://spaceprojects.arc.nasa.gov/Sp...er/PNStat.html

Well, you realize my offering was 'pie in the sky', which would only become operative if the Newton G 'constant' proved incontinent at the far end of our solar system. The Oort Cloud is still many AU's past the Kuiper Belt, maybe half way to our nearest star. As you point out, past the half-way mark, the next star takes over and puts a drag on Pioneer or Voyager, to capture it into its own 'Ooort cloud' distant orbit. (I'm assuming all stars have this distant region, if G is not a constant but greater farther out.). My point is that it may be much more difficult to achieve a linear trajectory in the medium of gravity variant space, given how much stuff is out there to effect this gravity, that it makes Einstein's space 'curvature' look pretty flat by contrast. That's why I think our distant probes, now coasting on their own momentum, may not have enough initial thrust to send them much further than the Oort Cloud, if (and only if) the Newton gravitational universal constant is not, and I mean not constant, but actually increases the further we get from a hot star. In the very cold of deep space, G may be a very big number, much more than the very tolerable 6.67e-11 Nm^2kg^-2 we experience here. Blue sky for now, however, until we have evidence that G ain't a universal constant as now assumed. Naturally, if we discover G is lower here and greater there, everything changes in astronomy, physics, theory, and Newton constants, and Einstein space-time. Remarkably, should this prove so, it will actually simplify physics! :P

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Caveat Lector. Experimentum summus judex...

MOND suggests a modification of G (I think) on galactic scales, but it's only a very small one. I would think orders-of-magnitude variances in G would be evident by now one way or another: stars orbiting the galaxy, comets returning sooner than expected, etc.

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Everything I need to know I learned through Googling.

I would have thought they would have seen any G differences by now too, so I'm with you there. MOND's modification is too small to effect real influence on Pioneers, in my opinion. G's variability would have to be orders above that.

One reason I suspect they had not guessed at a variable G was because it was never obvious. So if it is not a universal constant, as we now assume it is, but proves to be something else, then it means we've been duped by Mother Nature, who is loathe to release her secrets wantonly, into believing an illusion. How could that be? The only way I can imagine this, other than the fact that we estimate all distant mass per its behavior vis a vis Newton's orbital equation, is if something happens to that mass in different G regions: greater G would mean our mass estimates for those regions are higher than they should be, BUT their inertial mass are greater, so they balance out. Hence, we never noticed. This is the only way it would make rational sense to me. Of course, Mother Nature may not be rational on her end!

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Caveat Lector. Experimentum summus judex...

There is actually a resultant apparent acceleration if you misjudge the spacecraft distance by an amount corresponding to the distance the spacecraft travels whilst the signal is on its way (as argued on my webpage Speed of Light and Theory of Relativity):

the distance mismatch at distance S(t) is
(1) s=-S(t)*V(t)/c
where V(t) is the spacecraft velocity.

From this you can calculate the apparent acceleration
(2) a(t)=d^2s/dt^2; = - 1/c*d^2(S(t)*V(t))/dt^2;

If you evaluate the differential you get
(3) a(t)=-A(t)*3*V(t)/c - S(t)/c*dA(t)/dt,
where A(t)=dV(t)/dt is the original acceleration due to whatever forces are acting on the probe.
If you assume A(t) to be given just by the gravitational field of the sun's mass M ,i.e.
(4) A(t)=GM/S^2(t),
and assume that V is roughly constant over the considered range, i.e.
(5) S(t)=V*t ,
one finds that the second term in Eq.(3)
(6) S(t)/c*dA(t)/dt = -2*A(t)*V/c ,
and therefore from (3)
(7) a(t)=-A(t)*V/c .

If you insert now for instance for A(t) the sun's gravitational acceleration at a distance of 20 AU and assume v=20 km/sec to be the average relative velocity between the probe and earth, you get

a(20AU)=-9.8*10^-8 cm/sec^2 ,

and at 60 AU
a(60AU)=-1.1*10^-8 cm/sec^2

The acceleration has therefore the observed order of magnitude but decreases with distance and is directed away from the sun. If one subtracts this acceleration from the constant observed acceleration of +8*10^-8 cm/sec^2, one obtains

a(20AU)(data)=1.7*10^-7 cm/sec^2 ,

and at 60 AU
a(60AU)(data)=9*10^-8 cm/sec^2

Corrected for the error due to the signal propagation, the anomalous acceleration is now not constant anymore (as diplayed in Andersons et al.'s analysis) but decreases with distance. This should substantially alter the situation regarding which effects might be responsible.

However, I would also like to mention that Anderson et al. quote the statistical error of the measurements as
2*10^-8 cm/sec^2 . This is actually not much smaller than the alleged anomalous acceleration, so one has to ask if there has probably a constant factor been neglected in the analysis and the whole effect is not some statistical noise.

Cool! I'll go over yours some more, since it seems to come up pretty close. My looking into this matter came up a little different from yours:

I had figured out independently that the Newton gravitational 'constant' G grows at the rate of about 7.3x10^-11 per AU, or approximately per 150x10^6 km. If you take this delta G and divide it by one AU in meters, you get:

7.3e-11/ 150e9 m = 0.048667e-20, or = 4.8667e-22 G/m

Now, assuming G is actually linear (ie., d/d^2 = 1/d) and growing at this rate, where it about doubles per AU (leaving aside for now the obvious problem, of why didn't we see this before?) then if you divide this growth rate by Earth's 'universal' G you get:

4.8667e-18/ 6.67e-11 = 0.7297e-7 m.s^-2, which is also = ~7.3e-8 m/s^2, or in centimeters it becomes: (delta) G/ (universal?) G = ~7.3e-10 cm.s^-2

Notice how close this is to the LANL study's acceleration towards the Sun: ~8x10^-8 cm/s^2. (vs. 7.3e-10 cm/s^2, room for systemic factors)**

So this does not prove anything, except that there may be more than one explanation of why these distant crafts are slowing. It could also be due to onboard factors, such as heat radiation, but I doubt these would be enough to cause the acceleration (really deceleration) of such a consistent magnitude. Of course, I could be wrong, but it seems to point to something not being quite right out there at 39+ AU, where they are now past Pluto. Too bad they can't 'talk' anymore!

Still, I am intrigued by yours, except that the calculations I read about say the acceleration is constant, not variable. In my opinion, this is truly worthy of further study, but I do stocks and bonds for a living, so am not up to it more than this.

Cheers, Ivan

**(edited for minus power error in original)

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Caveat Lector. Experimentum summus judex...

Considering that we have probes travel for years in the Solar System and we still can get them to land where we planned, I have my doubts about this explanation.

As far as I understand, the velocity of the probe is measured from the Doppler shift of the signal, and the effect does not depend on the distance.
Why would they assume that the travel time of the signal depends on the velocity?

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

Ivan, I am sure a corresponding variation in G would have been detected already long ago from the motion of planets for instance.

The time for the signal to reach the spacecraft is traditionally calculated through the equation
(1) T=(S+V*T)/c
where S is the distance of the spacecraft at the moment the signal is sent out, V the velocity of the spacecraft and c the speed of light. This means that
(2) S=(c-V)*T.
However this equation contradicts the principle of the invariance of c which implies that a vectorial addition of c and V is not allowed (I have detailed this on my page http://www.physicsmyths.org.uk/lightspeed.htm ).
The invariance of c would imply instead
(3) S=c*T
which means that (2) underestimates the distance by an amount
(4) s=-V*T = -S*V/c (using (3))

As shown in my mathematical derivation above, from this it follows that the acceleration A (due to the gravitational influence of the sun) is correspondingly overestimated by an amount
(5) a= -A*V/c .

Both (4) and (5) give the right order of magnitude for the observed mismatches of the distance and acceleration but they depend on the distance and they have the wrong sign. It does therefore not fully explain the data as these show an anomalous acceleration constant with distance, but if the effect is taken into account, the data would then be not constant anymore but show a decrease with distance (as shown numerically above).

Regarding your argument that we can still land spacecraft on other planets: all missions involve frequent corrections to the orbit in order to account for all kinds of known and unknown influences. This is likely to mask any systematic error in the determination of the trajectory.

Which is the distance of the probe when the signal was emitted form Earth.
If the probe is travelling with constant velocity V (as you assumed for simplicity in eq. (1)), the distance probe-Earth when the signal is recieved by the probe is given by:

(2bis) S + V*T = c*T - V*T + V*T = c*T

which is exactly what eq. (1) implied (meaning that T is defined as distance probe-Earth divided by c).

Wrong, because (c - V) is not the speed of the signal as observed by the probe.
The speed of the signal as observed by the probe is still c, but the probe is moving and the signal has to catch up (having a finite speed).
Hence eq. (2bis), where to the distance S we need to add the distance V*T (the distance the probe gained while the signal covered the distance S).

But in eq. (1) you defined implicitly T as the time necessary for the signal to go from Earth to the moving probe.
The signal started when the probe was at distance S, and the signal reached it when the probe was in S+V*T.
So, eq. (3) is wrong because the term V*T has been omitted.


Sorry, but your mathematical derivation is wrong.

What you have done is:
1) assume a=b (eq. (1));
2) assume a=c (eq. (3));
3) but b is not c, therefore the theory is wrong.

You used contraddictory assumptions, so it is no wonder that you get contraddictory results.

Trajectories that have been computed beforehand.

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

You misunderstood my argument:
Eq.(1) is not the one used by me but it would have been used in the analysis of the Pioneer data. I used Eq.(3) instead.
Let my try to make the situation clearer:

Assume the spacecraft is at distance S. Consider first it is stationary relative to the earth and that one uses not light but particles with speed C for communication. These would reach the probe after time
T=S/C.
Now assume instead the spacecraft is receding with velocity V. The particles would then reach the probe after time
T=S/(C-V)
because the velocity of the spacecraft and the particles add vectorially.
Now exactly the same equations are assumed to hold also if one uses light for communication, but this violates the fact that the propagation of light has to be independent of the reference frame and the speed of light c can not be added vectorially to V. Instead on has to assume that the time to reach the spaceprobe does not depend on V at all, i.e.
T=S/c
as for the resting spacecraft.
Of course the spacecraft has travelled the additional distance V*T in the meanwhile, but the signal has nevertheless caught up with it after time T=S/c and not after T=S/(c-V). If you wrongly assume the latter (as NASA would do) you underestimate therefore the distance associated with time T by an amount V*T=S*V/c.

Let's see.

1) time = 0: probe is at distance = S from Earth and a signal is sent to the probe.

The probe is moving away from Earth with constant velocity V.

2) time = T: signal reaches S, but the probe is no longer there because it has moved.

3) time = T': signal reaches the probe.

The distance where the signal reaches the probe is S+S', where S' = V*T'.

In the frame of reference where the Earth is at rest, the distance probe-Earth increases while the signal is travelling towards the probe.
In the frame of reference where the probe is at rest, the same thing is observed.
The distance travelled by the signal is S+S' = c*T'.

So, S + S' = S + V*T' = c*T', which gives T' = S/(c-V).
We know that S = c*T, therefore T' = [c/(c-V)]*T > T.

Hence we have seen that the time necessary for the signal to reach the probe depends on the speed of the probe (because the distance is increasing).

What you said above is wrong (you said that T = T').

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

Papageno, just think about it again:
Consider the problem, as you suggested, from the viewpoint of the probe which is supposed to be at distance S when the signal is emitted (t=0). In this case the earth is receding from the probe with velocity V which however is obviously irrelevant for the question when the signal reaches the probe (nobody cares about the motion of the earth after the signal has been emitted). Also, it is known that the speed of light must be independent of the state of motion of the emitter at t=0 (invariance of c). The signal will therefore reach the probe in any case after time T=S/c and does not depend on V (the only effect of the velocity would be a corresponding Doppler shift of the light frequency).

#-o
It is late and I had a lot of brie at a party.

EDIT to add:
That particular statement is wrong, but not the rest of my post, since it is all observed from Earth.

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

I think since the same sunward accelleration is not bourne out by the Voyager project that the possible interaction with an unkown Kuiper belt object is more likely.

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Valiant Dancer

The Pioneers are going in very different directions but exhibit the same behavior - I don't think you can attribute it to a single Kuiper Belt object.

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Everything I need to know I learned through Googling.

If memmory serves correctly, Pioneer 10 shows the more pronounced effect of the accelleration than 11 did (until contact was lost). This could be from the angle from ecliptic which has the possibility of dragging the Pioneer project down due to multiple Kuiper object interactions than the steeper angle out of the ecliptic that the Voyager project took.

I in no way suggested that they were both due to a single Kuiper object.

Not.

The curves in Anderson's paper are hard to justify on the bases of interaction with a discrete object. It is possible this is an interaction with the entire Kepler belt in the region of the probes, but unless this function is nearly continuous, and that is not likely, the Kepler belt is not a good solution.

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jwj

It's a big universe out there...is it really unwinding, really burning out?

Thomas, you further responded to 'papageno' with: This is what I had always suspected, that there is some 'fudge' factor in how we reach our distant space destination, by frequent corrections to the orbit in order to account for all kinds of known and unknown influences, so our trajectoral computations in advance of launch are adjusted. This is not proof positive that something is wrong with our gavitational assumptions, but it is a clue.

The only way to make sense of this is that if the so-called constant G is higher for the outer planets, the inertial mass is also; the converse means that our planetary mass estimates are too high for local G conditions, though correct for the 'constant' G assumed, which is an Earth based assumption. If you use the orbital GM = Rv^2, then a higher G means a lower M, but you'll still get there! What this means is that the inertial mass on Earth is how the craft's mass was defined, but in a higher G region, as measured in local conditions, the craft's 'mass' becomes greater (locally only in terms of local G). This appears to be happening for Pioneers, and also noted to a lesser degree with Cassini. I realize this is a mind bender, but we never really looked for it, so merely adjusted the craft's progress along its trajectory, since the differences in G are fairly small over great distances, i.e., ~7.3e-11 Nm^2kg^-2 per AU, which yields a constant acceleration towards the Sun of about 7-8e-8 cm.s^-2, as mentioned above. The 'unknown influences' causing frequent in flight adjustments can be known, if this is so, though a whole new can of worms opens if G is different:

What would a non-constant G do to General Relativity's predictions, or present cosmology in general, if all of it assumes a constant G? So, if G is NOT constant... "Houston, we got a problem." :-?

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Caveat Lector. Experimentum summus judex...

It is clear that the way I phrased the response that people are interpreting it as a single Kuiper belt object. I meant no such interpretation and apologize for the misunderstanding. The reports that I have seen indicate a possible interaction with a Kuiper belt object and Pioneer 10. Both Pioneer project craft (10&11) seem to be being retarded by multiple kuiper belt object interactions due to the slight angle of thier trajectory from the ecliptic. The Voyager project, having a much steeper angle from the ecliptic, has no such anomalyous sunward accelleration.

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Valiant Dancer

So far every planetary system found is utterly unlike ours. It indicates that planets wander freely from their original point of formation.

So, I suggest that the reason our system has a nice pattern to the orbits is because the planets kept moving around until they fell into a configuration that was stable; and then stopped moving around and stayed the way we see.

Are you certain this is correct? It is my understanding that course and antenna aiming corrections introduce vaguaries in the orbital path of the Voyagers that may include an acceleration of the same order as the Pioneer probes, and certainly do not rule it out.

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jwj

It's a big universe out there...is it really unwinding, really burning out?

On the right-hand-side you have v^2.
If you change both G and M, this does not mean that the vectors R and V are the same.
And this does affect the motion of the probe.

The weight (i.e., the force) changes, why should the mass change?

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

http://www.space.com/scienceastronom...ay_041018.html

"He looked at the two Voyager spacecraft, also exiting the solar system, but says their design involved "numerous attitude-control maneuvers" that "can overwhelm the signal of a small external acceleration."" -- from the article.

I see your point. However, other probes with shallow ecliptic plane trajectories have shown the same anomalyous accelleration shift. There are several other probable reasons for that slow down than "the force of gravity is different over distance".

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Valiant Dancer

Yup, changes in G & M will affect motion results, since mass in a higher G environment has greater inertial mass. The M reading in a higher G region is consequently lower in local inertial terms of G, but this is very confusing, since we measure all mass in Earth's G, so not used to thinking in terms of 'local kilograms' which are greater than Earth kilograms, for the outer solar system. The mass does not change in terms of Earth's G, only 'appears' lower in local G, if this G is higher than here.

I think the vector Rv^2 can be treated as scalars, but not totally sure about that, so don't quote me here.

The operative here is in local conditions.

I'm going here with Haisch and Rueda's "Inertial mass and gravitational mass may be identical because they have an identical source process...", so inertial mass has G equivalence. Therefore, if G force changes, meaning the G 'constant' is greater, then inertial mass should be likewise greater.

The way I understand it is that the spacecraft's mass does not undergo any kind of change, except that if measured in local gravitational force, using local units, the mass is different in those units only. I realize we don't think this way because we never had to, but if G is a variable, then we have to do so now. Of course, this is all contingent on a rather big :roll: IF :roll:.

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Caveat Lector. Experimentum summus judex...

True statement.

I'm looking at it from a very different prospective. If gravity and inertia are truly equivalent - the same force, whether or not it is electromagnetic (which I think it is), - then there is no zero point field: Objects exhibit inertia because the necessary tensor inequalities have been established, just as Einstein envisioned them.

But without the zero point field, the tensors on the very edges of the galaxy thin. Inertial energy is radiated and lost as the impedance of empty space increases. This not only explains the MOND effect, it explains why galaxies are radio loud: the energy radiated is the broadcast of an impedance challenged 'inertial' vector.

If this is the way space works, we shouldn't be surprised if gravity 'appears' stronger with increasing distance from the sun as the 'inertial' vector diminishes relative to the mass of these objects. However, if the pioneer probes are not following kepler orbits, neither should other relatively low mass objects, like pluto, and perhaps even neptune...

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jwj

It's a big universe out there...is it really unwinding, really burning out?

In particular: if the pioneer probes are not following kepler orbits... This may be a case of comparing a vehicle launched from Earth and 'vehicles' in orbit for millions of years, the distant planets. One would expect them to behave the same, but it does not have to be so. What Pluto is not doing is traveling along a path cutting through all these solar orbits, traveling out of the solar system, while the Pioneers are. So there is a fundamental difference.

Remember that we only estimate Pluto's mass, based on how it orbits, but we have no way of knowing what that mass really is, nor the planet's density. And now, even its gravitational description may be in doubt. But Pluto's, or Neptune's orbits are relatively stable, though some think Pluto is a former Neptune moon, but overall they are where their orbits settled them. This is why I said earlier that if G is a growing force out there, then very likely as Pioneers slow further they will find their stable orbits very far out. My guess is beyond the Kuiper Belt, out somewhere in the Oort cloud, which I also think is a kind of cosmic graveyard.

I don't follow, however: we shouldn't be surprised if gravity 'appears' stronger with increasing distance from the sun as the 'inertial' vector diminishes relative to the mass of these objects. Do you mean what Thomas is saying, that we are measuring it with a c-v signal?

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Caveat Lector. Experimentum summus judex...